Age of Information Minimization for Grant-Free Non-Orthogonal Massive Access Using Mean-Field Games

NOMA Versus OMA: Scheduling to Minimize the Age of Information

“…Similar approach follows for the expected system throughput. In Lemma 2, after substituting 𝑞 𝑂 𝑖 , 𝑝 𝑁 1→2 and 𝑝 𝑁 2→1 from ( 5) and ( 6), respectively, into (3) and ( 4), and further simplifying, we can obtain (7) and (9), respectively. The proof of Corollary 2.1 follows from Lemma 2 as lim 𝜌→∞ Γ 𝑆 = 1 2 and lim 𝜌→∞ Γ 𝐴 = 1 2 and the exponential functions in Γ 𝑆 and Γ 𝐴 have monotonic behaviour in 𝜌.…”

Age‐optimal design for UAV‐assisted grant‐free non‐orthogonal massive access: Mean‐field game approach

“…In this network, these IoT devices are monitoring environmental conditions and needs to update these information to the UAV in a real‐time manner since potential delay might cause severe damage. Therefore, IoT devices will transmit the generated data packet to the UAV immediately [23]. The UAV owns K orthogonal channels, denoted by $$\mathcal {K} = \lbrace 1, \ldots , K\rbrace$$, to support the massive access of these IoT devices.…”

“…With these notations and observations, we can have the following proposition in terms of the outage probability according to ref. [23]. Proposition When the number of IoT devices over channel k is $$C_k$$, the expected number of interfering packets to one packet can be written as $$\begin{equation} I_k = \frac{2T_p}{T_s - T_p} C_k.$$…”

“…With this metric, we can derive how the distribution changes with the potential function, which is called the Fokker–Planck equation, as given in the following proposition [23]. Proposition Given the strategy graph $$\mathcal {G}$$ and a continuous utility function $$\tilde{U}^f(\bm {\rho }(t))$$, for an initial distribution $$\bm {\rho }_0$$, the Fokker–Planck equation can be written as $$\begin{equation} \frac{{\rm {d}} \rho ^i(t)}{{\rm {d}} t} = \sum \limits _{j \in \mathcal {N}(i)}\theta ^{ij}(\bm {\rho }(t))[\tilde{U}^f_i(\bm {\rho }(t)) - \tilde{U}^f_j(\bm {\rho }(t))], \end{equation}$$where $$ \mathcal {N}(i) = \lbrace j \in \mathcal {S}: (i,j) \in \mathcal {E}\rbrace$$ is the neighbouring set of vertex i in $$\mathcal {G}$$.…”

NOMA Versus OMA: Scheduling to Minimize the Age of Information

“…Physical layer network coding enabled NOMA has been proposed in [5] to minimize AoI. In contrast to these works, [6] and [7] have proposed AoI-independent scheduling schemes for NOMA in decentralized setting of slotted ALOHA and grant-free massive access, respectively.…”